1 Introduction

This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various countries \(m\) of the world. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodolgy and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was b2d1326344a351575a5aff7c5a16704dca3d8302.

2 Data

Data are downloaded from ???. Minor formatting is applied to get the data ready for further processing.

3 Basic Exploration

Below we plot cumulative case count on a log scale by continent. Note that “Other” relates to ships.

Reported Cases by Continent

Reported Cases by Continent

Below we plot the cumulative deaths by country on a log scale:

Reported Deaths by Continent

Reported Deaths by Continent

4 Method & Assumptions

The methodology is described in detail here. We filter out countries with populations of greater than 500 000. Weeks where the deaths or cases are not greater than 50 are left out of results.

5 Results

5.1 Current \(R_{t,m}\) estimates by country

Below current (last weekly) \(R_{t,m}\) estimates are plotted on a world map.

5.1.0.1 Cases

5.1.1 Deaths

5.2 Top 10 countries

Below we show various extremes of \(R_{t,m}\) where counts (deaths or cases) exceed 50 in the last week.

5.2.1 Lowest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Australia deaths 54 2020-09-13 0.4 0.5 0.7
Ecuador deaths 53 2020-12-22 0.4 0.6 0.8
Kyrgyzstan deaths 51 2020-08-11 0.4 0.6 0.8
Nepal deaths 59 2020-12-24 0.5 0.7 0.9
Argentina deaths 780 2020-12-24 0.7 0.7 0.8
Sudan deaths 60 2020-12-24 0.6 0.7 0.9
Oman deaths 52 2020-11-10 0.6 0.7 1.0
Bulgaria deaths 684 2020-12-24 0.7 0.7 0.8
Kosovo deaths 59 2020-12-21 0.6 0.8 1.0
Spain deaths 1,047 2020-12-24 0.7 0.8 0.8

5.2.2 Lowest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Central African Republic cases 51 2020-07-27 0.2 0.3 0.3
Yemen cases 51 2020-12-13 0.2 0.3 0.4
Mauritius cases 51 2020-04-15 0.3 0.4 0.6
Gambia cases 51 2020-09-26 0.3 0.4 0.6
Turkey cases 145,032 2020-12-24 0.4 0.5 0.7
Ghana cases 490 2020-12-24 0.6 0.6 0.7
Luxembourg cases 1,930 2020-12-24 0.6 0.6 0.7
Bulgaria cases 8,370 2020-12-24 0.6 0.7 0.7
Sudan cases 1,051 2020-12-24 0.6 0.7 0.7
Azerbaijan cases 18,601 2020-12-24 0.7 0.7 0.7

5.2.3 Highest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Democratic Republic of Congo deaths 207 2020-12-24 6.8 11.6 14.2
Cameroon deaths 91 2020-06-21 1.4 1.8 2.4
Dominican Republic deaths 55 2020-10-08 1.1 1.5 1.9
South Africa deaths 1,972 2020-12-24 1.3 1.4 1.5
Denmark deaths 122 2020-12-24 1.2 1.4 1.7
Egypt deaths 245 2020-12-24 1.2 1.4 1.6
Luxembourg deaths 61 2020-12-16 1.1 1.4 1.8
Finland deaths 52 2020-12-23 1.0 1.4 1.8
South Korea deaths 128 2020-12-24 1.1 1.4 1.6
China deaths 1,290 2020-04-23 1.1 1.3 1.6

5.2.4 Highest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
South Sudan cases 233 2020-12-24 5.4 7.2 8.6
Bhutan cases 79 2020-12-24 3.1 5.8 10.5
Eritrea cases 210 2020-12-24 2.3 3.0 3.7
Thailand cases 1,613 2020-12-24 1.8 2.6 4.1
Comoros cases 72 2020-12-24 1.8 2.5 3.4
Suriname cases 382 2020-12-24 1.9 2.4 3.0
Congo cases 371 2020-12-24 1.8 2.3 2.8
Mongolia cases 134 2020-12-24 1.5 2.1 2.8
Cambodia cases 55 2020-07-27 1.4 1.9 2.6
Papua New Guinea cases 76 2020-12-17 1.4 1.8 2.3

5.3 Risk Quadrants

The plots below show weekly cases (or deaths) on the X-axis and the reproduction number on the Y-axis. By dividing this into 4 quadrants we can identify countries with high cases and high reproduction numbers, or high cases and low reproduction numbers etc. Countries in the top right quadrant would be in trouble.

Values where the reproduction number exceeds 3 are plotted at 3.

5.3.1 Cases

5.3.2 Deaths

5.4 Country Plots by Continent

Below we plot results for each country/province in a list. Values larger than 3 are plotted at 3.

5.4.1 Africa

5.4.1.1 Angola

5.4.1.2 Burundi

5.4.1.3 Benin

5.4.1.4 Burkina Faso

5.4.1.5 Botswana

5.4.1.6 Central African Republic

5.4.1.7 Cote d’Ivoire

5.4.1.8 Cameroon

5.4.1.9 Democratic Republic of Congo

5.4.1.10 Congo

5.4.1.11 Comoros

5.4.1.12 Cape Verde

5.4.1.13 Djibouti

5.4.1.14 Algeria

5.4.1.15 Egypt

5.4.1.16 Eritrea

5.4.1.17 Ethiopia

5.4.1.18 Gabon

5.4.1.19 Ghana

5.4.1.20 Guinea

5.4.1.21 Gambia

5.4.1.22 Guinea-Bissau

5.4.1.23 Equatorial Guinea

5.4.1.24 Kenya

5.4.1.25 Liberia

5.4.1.26 Libya

5.4.1.27 Lesotho

5.4.1.28 Morocco

5.4.1.29 Madagascar

5.4.1.30 Mali

5.4.1.31 Mozambique

5.4.1.32 Mauritania

5.4.1.33 Mauritius

5.4.1.34 Malawi

5.4.1.35 Namibia

5.4.1.36 Niger

5.4.1.37 Nigeria

5.4.1.38 Rwanda

5.4.1.39 Sudan

5.4.1.40 Senegal

5.4.1.41 Sierra Leone

5.4.1.42 Somalia

5.4.1.43 South Sudan

5.4.1.44 Eswatini

5.4.1.45 Chad

5.4.1.46 Togo

5.4.1.47 Tunisia

5.4.1.48 Tanzania

5.4.1.49 Uganda

5.4.1.50 South Africa

5.4.1.51 Zambia

5.4.1.52 Zimbabwe

5.4.2 Asia

5.4.2.1 Afghanistan

5.4.2.2 United Arab Emirates

5.4.2.3 Armenia

5.4.2.4 Azerbaijan

5.4.2.5 Bangladesh

5.4.2.6 Bahrain

5.4.2.7 Bhutan

5.4.2.8 China

5.4.2.9 Georgia

5.4.2.10 Indonesia

5.4.2.11 India

5.4.2.12 Iran

5.4.2.13 Iraq

5.4.2.14 Israel

5.4.2.15 Jordan

5.4.2.16 Japan

5.4.2.17 Kazakhstan

5.4.2.18 Kyrgyzstan

5.4.2.19 Cambodia

5.4.2.20 South Korea

5.4.2.21 Kuwait

5.4.2.22 Lebanon

5.4.2.23 Sri Lanka

5.4.2.24 Maldives

5.4.2.25 Myanmar

5.4.2.26 Mongolia

5.4.2.27 Malaysia

5.4.2.28 Nepal

5.4.2.29 Oman

5.4.2.30 Pakistan

5.4.2.31 Philippines

5.4.2.32 Palestine

5.4.2.33 Qatar

5.4.2.34 Saudi Arabia

5.4.2.35 Singapore

5.4.2.36 Syria

5.4.2.37 Thailand

5.4.2.38 Tajikistan

5.4.2.39 Turkey

5.4.2.40 Taiwan

5.4.2.41 Uzbekistan

5.4.2.42 Vietnam

5.4.2.43 Yemen

5.4.3 Europe

5.4.3.1 Albania

5.4.3.2 Austria

5.4.3.3 Belgium

5.4.3.4 Bulgaria

5.4.3.5 Bosnia and Herzegovina

5.4.3.6 Belarus

5.4.3.7 Switzerland

5.4.3.8 Cyprus

5.4.3.9 Czechia

5.4.3.10 Germany

5.4.3.11 Denmark

5.4.3.12 Spain

5.4.3.13 Estonia

5.4.3.14 Finland

5.4.3.15 France

5.4.3.16 United Kingdom

5.4.3.17 Greece

5.4.3.18 Croatia

5.4.3.19 Hungary

5.4.3.20 Ireland

5.4.3.21 Italy

5.4.3.22 Lithuania

5.4.3.23 Luxembourg

5.4.3.24 Latvia

5.4.3.25 Moldova

5.4.3.26 North Macedonia

5.4.3.27 Montenegro

5.4.3.28 Netherlands

5.4.3.29 Norway

5.4.3.30 Kosovo

5.4.3.31 Poland

5.4.3.32 Portugal

5.4.3.33 Romania

5.4.3.34 Russia

5.4.3.35 Serbia

5.4.3.36 Slovakia

5.4.3.37 Slovenia

5.4.3.38 Sweden

5.4.3.39 Ukraine

5.4.4 North America

5.4.4.1 Canada

5.4.4.2 Costa Rica

5.4.4.3 Cuba

5.4.4.4 Dominican Republic

5.4.4.5 Guatemala

5.4.4.6 Honduras

5.4.4.7 Haiti

5.4.4.8 Jamaica

5.4.4.9 Mexico

5.4.4.10 Nicaragua

5.4.4.11 Panama

5.4.4.12 El Salvador

5.4.4.13 Trinidad and Tobago

5.4.4.14 United States

5.4.5 Oceania

5.4.5.1 Australia

5.4.5.2 New Zealand

5.4.5.3 Papua New Guinea

5.4.6 South America

5.4.6.1 Argentina

5.4.6.2 Bolivia

5.4.6.3 Brazil

5.4.6.4 Chile

5.4.6.5 Colombia

5.4.6.6 Ecuador

5.4.6.7 Guyana

5.4.6.8 Peru

5.4.6.9 Paraguay

5.4.6.10 Suriname

5.4.6.11 Uruguay

5.4.6.12 Venezuela

5.5 Detailed Output

Detailed output for all countries are saved to a comma-separated value file. The file can be found here.

6 Discussion

Limitation of this method to estimate \(R_{t,m}\) are noted in [1]

  • It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
  • It relies on an assumed generation interval assumptions.
  • The size of the time window can affect the volatility of results.
  • Results are time lagged with regards to true infection, more so in the case of the use of deaths.
  • It’s sensitive to changes in case (or death) detection.
  • The generation interval may change over time.

Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.

Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

7 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Head of Research & Analytics
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

References

[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133

[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim